Let $G$ be an amenable countable group. Why does every subgroup and homomorphic image of $G$ is amenable? Further more, if $N$ is a normal subgroup of $G$, and both $N$ and $G/N$ are amenable, why does $G$ must be amenable?
2026-02-23 07:59:11.1771833551
Properties of amenable groups
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V. Runde, Lectures on Amenability. Springer, 2002 (Lecture notes in mathematics ; 1774). Section 2.3 "Hereditary properties"